My current research areas include Rough sets, Algebra, Logic, Vagueness, Soft
Computing, Mereology, Algebraic Logic, Ontology, Dialectical Logics, Ordered
Structures, Partial Algebras, Foundations of Mathematics, Education Research, Philosophical Logic,
Fuzzy Sets and Theory of Knowledge I have interests in applications to social
social sciences, feminism, gender studies and applied philosophy too. You can
request a *not-so-short research statement* to know more.

Most of my recent publications have been in the area of foundations of rough sets and algebraic logic. My research in rough sets range over axiomatic approach to granularity, various algebraic semantics of rough sets, Contamination problem, Knowledge, rationality, rough number systems, and connections with probability and fuzzy sets in particular. Specifically I have also invented/worked on high granular operator spaces (partial algebras), adaptation of rough semantics to Posets with difference, higher order semantics for classical rough set theory, AntiChain based Semantics, Tolerance Approximation Spaces, Granular Rough Semantics, Variable Precision Rough Sets, Irreflexive Rough Sets, Bitten RST (in TAS), Logic of TQBA and Variants, Problem of Combining Generalized Rough Semantics, Dialectical Rough Logics, Rough Theory of Knowledge, Integrated (of multiple meta levels) Rough Semantics, Mereology, ideal based rough sets and applications in algebra and logic.

Click on the link below for a list of my recent publications. A few of them can be found at Arxiv.

Before 1996, I used to work on fixed point theory, summability, topology, posets and semigroups mainly. I have published quite a bit on feminism, and trans feminist issues. These can be found in my feminist research page.

I am, of course, very good in philosophy. Some of the meta principles due to myself (in a interpretation) that I try to stick to:

- There is no one handle to hold on to the Mathematics of Vagueness.
- Among branches of mathematics and materialism, no branch forms an island isolated from other branches and the relation of relatedness among different branches tends to change across problem perspectives. There are ways of working relative to the idea of problem perspectives themselves so that the relatedness may be stable or unstable. This should be the way.
- Given a collection of relatively rough and crisp objects (real and virtual) in a semantic domain, a useful goal can be to derive a rough evolution of the state of affairs that is as unambiguous as is possible.

I have been working on three different monographs on algebra, order and logics for quite some time. These are delayed due to my pre-occupation with research papers and other matters.

My co-edited research volume on "Algebraic Methods in General Rough Sets" has appeared in the Springer Trends in Mathematics Series . The springer page is here. The CFP was at easychair and at the rough set society website. The book includes the following research chapters:

- Part-1
- Ch1: Mani, A., Cattaneo, G. and Düntsch, I.: Introduction, Pages 1-11
- Ch2: Gianpiero Cattaneo: Algebraic Methods for Rough Approximation Spaces by Lattice Interior-Closure Operations: 13-156
- Ch3: Mani A: Algebraic Methods for Granular Rough Sets: 157-335
- Ch4: Piero Pagliani: Three Lessons on the Topological and Algebraic Hidden Core of Rough Set Theory: 337-415
- Ch5: Jouni J{\"a}rvinen and S{\'a}ndor Radelecki: Irredundant Coverings, Tolerances, and Related Algebras: 417-457
- Ch6: Mani A: Algebraic Representation, Dualities and Beyond: 459-552
- Ch7: Gianpiero Cattaneo and Davide Ciucci: Algebraic Methods for Orthopairs and induced Rough Approximation Spaces: 553-640
- Part-2
- Ch8: Patrik Eklund and Maria \'Angeles G\'alen: Rough objects in monoidal closed categories: 641-655
- Ch9: Bijan Davvaz: Rough Algebraic Structures Corresponding to Ring Theory: 657-695
- Ch10: Ali Shakibah: S-Approximation Spaces: 697-725

I did a rather late doctorate in mathematics. A compact version (306pp, a4) of my thesis is available here . It includes some of my work done before the year 2015, in algebraic semantics of general rough sets including those arising from generalized transitive relations, knowledge interpretation and related semantics, and axiomatic approach to granularity, contamination problems and related measures. A library/print copy can be ordered from pothi.com.

My list of collaborators is quite long. Almost everybody working on the foundations of rough sets is a collaborator. I have collaborators in algebra, formal logic, FOM, applied areas and communities like IRSS, CLC, ALI, WIL, AWM, WIM, and ISRS too.

Link to my research gate page.

I have published quite a bit on feminism, and trans feminist issues. These are often from an interdisciplinary perspective and can be found in my feminist research page.